As shown in tab:payoff, when the follower leaves the market, the leader gets 1; otherwise, 0, and hence the leader's objective is to drive the follower out of the market. On the other hand, the follower's goal is to survive in the market by avoiding competition with the leader. From the payoff matrices, to defeat the follower of type \(\theta _1\) , the leader has to commit to a mixed strategy that allows her to play \(i_1\)  at least with probability \(2/3\) . Similarly, to force the type \(\theta _2\)  to leave the market, the leader has to play \(i_2\)  with a probability of at least \(1/2\) . There does not exist a mixed strategy that drives both types out of the market, and the optimal leader's strategy in this Bayesian Stackelberg game is to play \(i_1\)  at least with probability \(2/3\) , which makes the type \(\theta _1\)  leaves the market, as the follower of this type occurs with a higher probability. The leader expected utility is \(0.55\)  under this Bayesian Stackelberg equilibrium (BSE). Without loss of generality, we assume that the follower breaks the ties in favor of the leader. The assumption is common in Stackelberg games [1]}. Generally, the leader can induce the follower to best respond to the leader's benefit by infinitesimal strategy variations. The corresponding solution concept is referred to as the strong Stackelberg equilibrium [2]}.
